Post Outline

Part 1 Recap

Part 2 Goals

Jupyter (IPython) Notebook

References

part 1 recap

In part 1 of this series we got a feel for Markov Models, Hidden Markov Models, and their applications. We went through the process of using a hidden Markov model to solve a toy problem involving a pet dog. We concluded the article by going through a high level quant finance application of Gaussian mixture models to detect historical regimes.

part 2 goals

In this post, my goal is to impart a basic understanding of the expectation maximization algorithm which, not only forms the basis of several machine learning algorithms, including K-Means, and Gaussian mixture models, but also has lots of applications beyond finance. We will also cover the K-Means algorithm which is a form of EM, and its weaknesses. Finally we will discuss how Gaussian mixture models improve on several of K-Means weaknesses.

This post is structured as a Jupyter (IPython) Notebook. I used several different resources\references and tried to give proper credit. Please contact me if you find errors, have suggestions, or if any sources were not attributed correctly.